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In the adjoining figure, OX =1/2XY, PX =...

In the adjoining figure, `OX =1/2XY, PX =1/2XZ `and OX =PX. Show that XY= XZ

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Given, `OX=(1)/(2)XYrArr2OX=XY` "... (i)
`PX=(1)/(2)XZrArr2PX=XZ` ...(ii)
and OX=PX …(iii)
According to Euclid's axiom, things which are double of the same things are equal to one another.
On multiplying Eq. (iii) by 2, we get
2OX=2PX
`rArr` XY=XZ `["from Eqs. ("i)and (ii)]`
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